不可压缩Navier-Stokes极限：相对论Boltzmann方程的最优收敛率
Incompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate
- School of Mathematics, Guangxi University（广西大学数学学院）
- Center for Applied Mathematical of Guangxi (Guangxi University)（广西应用数学中心（广西大学））
- Post-doctoral Research Station of the First-level Discipline in Mathematics, Guangxi University（广西大学数学一级学科博士后科研流动站）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过谱分析和Duhamel原理，证明了相对论Boltzmann方程经典解在扩散极限下收敛到不可压缩Navier-Stokes系统解，首次给出最优收敛率及初始层精确估计，并建立了全局强解的存在唯一性。
AI中文摘要：
我们研究了初值接近全局相对论Maxwellian分布的相对论Boltzmann方程经典解的扩散极限。通过谱分析，我们建立了相对论Boltzmann方程经典解到不可压缩Navier-Stokes系统解的收敛性，并首次给出了最优收敛率和初始层的精确估计。此外，通过对线性碰撞算子$L$的精细分析，结合Duhamel原理，我们获得了相对论Boltzmann方程全局强解的存在唯一性，以及一个与光速$\mathbf{c}$无关的收敛率。
英文摘要：
We study the diffusion limit of the classical solution to the relativistic Boltzmann equation with the initial data near a global relativistic Maxwellian. By using spectral analysis, we establish the convergence of the classical solution to the relativistic Boltzmann equation to that of the incompressible Navier-Stokes system, and give for the first time the optimal convergence rate and a precise estimate of the initial layer. Moreover, through a refined analysis of the linear collision operator $L$, combined with Duhamel's principle, we obtain the existence and uniqueness of a global strong solution to the relativistic Boltzmann equation, as well as a convergence rate independent of the speed of light $\mathbf{c}.$
